Question

In the figure below, a circle with centre O is inscribed inside ALMN. A and B are the points of tangency.

Find \(\angle ANB\)

Answer 1

Given, major ∠AOB = 260°

Minor ∠AOB = 360° - 260° = 100°

We know that radius and tangent are perpendicular. So, 

∠NAO =∠NBO = 90°

In a quadrilateral NAOB,

 ∠NAO + ∠AOB + ∠NBO + ∠ANB = 360°

90° + 100° + 90° + ∠ANB = 360°

∠ANB = 360° - 280°

⇒∠ANB = 80°

Hence, the value of ∠ANB is 80°.